| a point at which a given function of a complex variable has no derivative but of which every neighborhood contains points at which the function has derivatives. |
sin·gu·lar·i·ty  (sĭng'gyə-lār'ĭ-tē)  n. pl. sin·gu·lar·i·ties
|
| singular point n. See singularity. |
singular point
of a function of the complex variable z is a point at which it is not analytic (that is, the function cannot be expressed as an infinite series in powers of z) although, at points arbitrarily close to the singularity, the function may be analytic, in which case it is called an isolated singularity. In general, because a function behaves in an anomalous manner at singular points, singularities must be treated separately when analyzing the function, or mathematical model, in which they appear.
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